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MathGroup Archive 2005

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Re: does a matrix equivalent of the Arg function exist?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53601] Re: does a matrix equivalent of the Arg function exist?
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 20 Jan 2005 03:47:42 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <csl1af$6su$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

at least quaternions have a representation with angle and a 3d vector,
but you can always define more than a single angle and for quaternions
you may describe the 3d vector by the absolute value and the two angles
of spherical coordinates, i.e.

q={r*Cos[psi],r*Sin[psi]*Cos[phi]*Sin[theta],r*Sin[psi]*Sin[phi]*Sin[theta],r*Sin[psi]*Cos[theta]}

Regards
  Jens

"Roger Bagula" <tftn at earthlink.net> schrieb im Newsbeitrag 
news:csl1af$6su$1 at smc.vnet.net...
> Arg[x+I*y] exists for any complex number.
> The 2by2 Matrix:
> {{x,-y},{y,x}}
> behaves very much like the complex number.
> With Euler matrices being three rotations by angles such that a total
> angle exists,
> it seems that an angle equivalency function like Arg should exist
> generally for nbyn matrices as a kind of measure like the determinant.
> Has anyone heard of such a matrix measure?
> Any ideas about how to form such a function?
> It would be useful geometrically in things like space and point groups
> used in
> crystalography and spectra of molecules.
> -- 
> Respectfully, Roger L. Bagula
> tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel:
> 619-5610814 :
> alternative email: rlbtftn at netscape.net
> URL :  http://home.earthlink.net/~tftn
> 



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